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Register a new userCompetition, Collaboration, and Optimization in Multiple Interacting Spreading Processes
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Competition and collaboration are at the heart of multi-agent probabilistic spreading processes. The battle on public opinion and competitive marketing campaigns are typical examples of the former, while the joint spread of multiple diseases such as HIV and tuberculosis demonstrates the latter. These spreads are influenced by the underlying network topology, the infection rates between network constituents, recovery rates and, equally importantly, the interactions between the spreading processes themselves. Here, for the first time we derive dynamic message-passing equations that provide an exact description of the dynamics of two interacting spreading processes on tree graphs, and develop systematic low-complexity models that predict the spread on general graphs. We also develop a theoretical framework for an optimal control of interacting spreading processes through an optimized resource allocation under budget constraints and within a finite time window. Derived algorithms can be used to maximize the desired spread in the presence of a rival competitive process, and to limit the spread through vaccination in the case of coupled infectious diseases. We demonstrate the efficacy of the framework and optimization method on both synthetic and real-world networks.
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Spreading processes have been largely studied in the literature, both analytically and by means of large-scale numerical simulations. These processes mainly include the propagation of diseases, rumors and information on top of a given population. In the last two decades, with the advent of modern network science, we have witnessed significant advances in this field of research. Here we review the main theoretical and numerical methods developed for the study of spreading processes on complex networked systems. Specifically, we formally define epidemic processes on single and multilayer networks and discuss in detail the main methods used to perform numerical simulations. Throughout the review, we classify spreading processes (disease and rumor models) into two classes according to the nature of time: (i) continuous-time and (ii) cellular automata approach, where the second one can be further divided into synchronous and asynchronous updating schemes. Our revision includes the heterogeneous mean-field, the quenched-mean field, and the pair quenched mean field approaches, as well as their respective simulation techniques, emphasizing similarities and differences among the different techniques. The content presented here offers a whole suite of methods to study epidemic-like processes in complex networks, both for researchers without previous experience in the subject and for experts.
A general formalism is introduced to allow the steady state of non-Markovian processes on networks to be reduced to equivalent Markovian processes on the same substrates. The example of an epidemic spreading process is considered in detail, where all the non-Markovian aspects are shown to be captured within a single parameter, the effective infection rate. Remarkably, this result is independent of the topology of the underlying network, as demonstrated by numerical simulations on two-dimensional lattices and various types of random networks. Furthermore, an analytic approximation for the effective infection rate is introduced, which enables the calculation of the critical point and of the critical exponents for the non-Markovian dynamics.
Recently, we introduced a quantity, node weight, to describe the collaboration sharing or competition gain of the elements in the collaboration-competition networks, which can be well described by bipartite graphs. We find that the node weight distributions of all the networks follow the so-called shifted power law (SPL). The common distribution function may indicate that the evolution of the collaboration and competition in very different systems obeys a general rule. In order to set up a base of the further investigations on the universal system evolution dynamics, we now present the definition of the networks and their node weights, the node weight distributions, as well as the evolution durations of 15 real world collaboration-competition systems which are belonging to diverse fields.
Recently, our group quantitatively defined two quantities, competition ability and uniqueness (Chin. Phys. Lett. 26 (2009) 058901) for a kind of cooperation-competition bipartite networks, where producers produce some products and output them to a market to make competition. Factories, universities or restaurants can serve as the examples. In the letter we presented an analytical conclusion that the competition ability was linearly dependent on the uniqueness in the trivial cases, where both the input quality and competition gain obey normal distributions. The competition between Chinese regional universities was taken as examples. In this article we discuss the abnormal cases where competition gains show the distributions near to power laws. In addition, we extend the study onto all the cooperation-competition bipartite networks and therefore redefine the competition ability. The empirical investigation of the competition ability dependence on the uniqueness in 15 real world collaboration-competition systems is presented, 14 of which belong to the general nontrivial cases. We find that the dependence generally follows the so-called shifted power law (SPL), but very near to power laws. The empirically obtained heterogeneity indexes of the distributions of competition ability and uniqueness are also presented. These empirical investigations will be used as a supplementary of a future paper, which will present the comparison and further discussions about the competition ability dependence on the uniqueness in the abnormal collaboration-competition systems and the relationship between the dependence and the competition ability and uniqueness heterogeneity.
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found that as in static networks, rewiring networks with degree distribution exponent $gamma >3$ exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For $2<gamma leq 3$ no such threshold exists, but for small infection rate the steady state density of infected nodes (prevalence) is smaller for rewiring networks.
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